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Series in optics and optoelectronics

Singularities and Vortices in Quantum Optics

Greg Gbur

Published Nov 22, 2016• 0 citations
Publisher

Abstract

Nowthat we have discussed the general structure and properties ofoptical vortices, we come to a pair of very practical questions: how do we generate pure vortex beams and how do we measure the characteristics of a vortex? As singular optics has grown as a eld, a variety of dierent methods have been introduced for both generation and detection, eachwith its own advantages and disadvantages. In this chapter, we summarize a number of these, beginning with the most common and progressing to the most esoteric.

DOI
10.1201/9781315374260-11

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Nowthat we have discussed the general structure and properties ofoptical vortices, we come to a pair of very practical questions: how do we generate pure vortex beams and how do we measure the characteristics of a vortex? As singular optics has grown as a eld, a variety of dierent methods have been introduced for both generation and detection, eachwith its own advantages and disadvantages. In this chapter, we summarize a number of these, beginning with the most common and progressing to the most esoteric.
In the previous chapters, we have seen that the cause of the mechanical effects of light on atoms is nothing more than the momentum exchanged between photons and atoms. This exchange determines both the forces exerted on atoms and, ultimately, the atoms’ translational motion. But now things become even more interesting. In this chapter we present to a new generation of laser beams that have been developed over the last few decades. These beams have quite unusual properties and even more exotic and fascinating applications. They contain optical vortices, as do many other physical systems, and, thus, are known as optical vortex beams.
Optical vortices are points of zero intensity in a two dimensional, classical optical field. As first discussed by Berry and Dennis [Berry, M. V. and Dennis, M. R., "Quantum cores of optical phase singularities" Journal of Optics A 6, S178-S180 (2004)] these singularities are replaced by 'quantum cores' in a deeper level of description. In a fully quantized theory of optical fields an excited atom trapped at the singularity can emit light spontaneously and hence soften the perfect zero of an optical vortex. More recently Barnett [Barnett, S. M., "On the quantum cores of a optical vortex," Journal of Modern Optics 55, 2279-2292 (2008)] presented a more realistic analysis of quantum cores which accounts for the effect of the trapping potential on the transition dynamics inside a vortex core. Here, we revisit the scenario of emission near an optical vortex in the realistic setting of Barnett.
A. Zeilinger proposed that photon pairs with entanglement of the orbital angular momentum (OAM) states could be detected in the course of spontaneous parametric down-conversion by illuminating a "fork" hologram (used for generating optical vortices) by a shifted Gaussian beam. Most closely related to the topic of this work are some early papers of the present authors. This chapter discusses both theoretically and experimentally, transformations of optical vortices which occur due to a complex Cartesian shift of the original functions of the complex amplitude. It theoretically and experimentally studies the transformation of the optical vortex proposed, by illuminating an amplitude "fork" hologram by a Gaussian beam with its waist center being shifted in the transverse plane from the hologram center. The chapter considers asymmetric Gaussian optical vortices that can be generated experimentally by diffraction of a Gaussian beam by an amplitude hologram with a typical "fork" at the point of singularity.
Methods to generate, manipulate, and measure optical and atomic fields with global or local angular momentum have a wide range of applications in both fundamental physics research and technology development. In optics, the engineering of angular momentum states of light can aid studies of orbital angular momentum (OAM) exchange between light and matter. The engineering of optical angular momentum states can also be used to increase the bandwidth of optical communications or serve as a means to distribute quantum keys, for example. Similar capabilities in Bose-Einstein condensates are being investigated to improve our understanding of superfluid dynamics, superconductivity, and turbulence, the last of which is widely considered to be one of most ubiquitous yet poorly understood subjects in physics. The first part of this two-part dissertation presents an analysis of techniques for measuring and manipulating quantized vortices in BECs. The second part of this dissertation presents theoretical and numerical analyses of new methods to engineer the OAM spectra of optical beams. The superfluid dynamics of a BEC are often well described by a nonlinear Schrodinger equation. The nonlinearity arises from interatomic scattering and enables BECs to support quantized vortices, which have quantized circulation and are fundamental structural elements of quantum turbulence. With the experimental tools to dynamically manipulate and measure quantized vortices, BECs are proving to be a useful medium for testing the theoretical predictions of quantum turbulence. In this dissertation we analyze a method for making minimally destructive in situ observations of quantized vortices in a BEC. Secondly, we numerically study a mechanism to imprint vortex dipoles in a BEC. With these advancements, more robust experiments of vortex dynamics and quantum turbulence will be within reach. A more complete understanding of quantum turbulence will enable principles of microscopic fluid flow to be related to the statistical properties of turbulence in a superfluid. In the second part of this dissertation we explore frequency mixing, a subset of nonlinear optical processes in which one or more input optical beam(s) are converted into one or more output beams with different optical frequencies. The ability of parametric nonlinear processes such as second harmonic generation or parametric amplification to manipulate the OAM spectra of optical beams is an active area of research. In a theoretical and numerical investigation, two complimentary methods for sculpting the OAM spectra are developed. The first method employs second harmonic generation with two non-collinear input beams to develop a broad spectrum of OAM states in an optical field. The second method utilizes parametric amplification with collinear input beams to develop an OAM-dependent gain or attenuation, termed dichroism for OAM, to effectively narrow the OAM spectrum of an optical beam. The theoretical principles developed in this dissertation enhance our understanding of how nonlinear processes can be used to engineer the OAM spectra of optical beams and could serve as methods to increase the bandwidth of an optical signal by multiplexing over a range of OAM states.